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Focusing on the historical evolution of connection and curvature, this graduate-level introduction to differential geometry caters to mathematics and physics students. It explores significant milestones such as Gauss' Theorema Egregium and the Gauss-Bonnet theorem while elucidating the Chern-Weil theory of characteristic classes on principal bundles. The book includes exercises to reinforce understanding and illustrates theoretical extensions. A foundational knowledge of manifolds and differential forms is essential, with de Rham cohomology required for the latter sections.
Nákup knihy
Differential Geometry, Loring W. Tu
- Jazyk
- Rok vydania
- 2017
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- Titul
- Differential Geometry
- Podtitul
- Connections, Curvature, and Characteristic Classes
- Jazyk
- anglicky
- Autori
- Loring W. Tu
- Vydavateľ
- Springer International Publishing
- Rok vydania
- 2017
- Väzba
- pevná
- Počet strán
- 368
- ISBN13
- 9783319550824
- Kategórie
- Matematika
- Anotácia
- Focusing on the historical evolution of connection and curvature, this graduate-level introduction to differential geometry caters to mathematics and physics students. It explores significant milestones such as Gauss' Theorema Egregium and the Gauss-Bonnet theorem while elucidating the Chern-Weil theory of characteristic classes on principal bundles. The book includes exercises to reinforce understanding and illustrates theoretical extensions. A foundational knowledge of manifolds and differential forms is essential, with de Rham cohomology required for the latter sections.